15.401 Recitation
8: Capital Budgeting
Learning Objectives

R i off Concepts
Review
C
t
o NPV
o Payyback Period
o IRR
o Profitability index

Examples
o Bart’s Super‐Widget*
2010 / Yichuan Liu
* Bart's Super‐Widget by Bart Raeymaekers
2
Review: capital budgeting

Decision:
o Accept or reject a project
o Compare two projects

D i ion rulle:
Decisi
o NPV, IRR, payback period, etc.

Information
o Cash flow projection
o Risk projection
o Tax
Ta reg
regulation
lation
2010 / Yichuan Liu
3
Review: NPV

Net present value (NPV) of a project is

CFt
NPV  
0
t
t 0 1 rt 
Decision should be based on after‐tax cash flow
instead of accounting earnings.
 Operating
O
ti profit
fit = operating
ti revenue – operating
ti
expenses without depreciation
 CF = (1 – τ) x operating profit – capital expenditure
+ τ x depreciation
((τ is the tax rate))

2010 / Yichuan Liu
4
Review: NPV

Decision rule:
o Independent projects: take all projects with NPV>0
o Mutually exclusive projects: take projects with the highest
NPVs
NPV

The NPV rule dominates all other rules because it
takes into account the maximum amount of
information, including timing of all cash flows and
risks, and makes the correct decision based on value
creation.
2010 / Yichuan Liu
5
Review: payback period

The payback period is the minimum T such that
T
 CF  CF
t 1
t
0
 I0
T is the minimum number of period required to
“recover” the initial investment, I0.
 Decisi
D i ion rule:
l

o Independent projects: take all projects with a payback
p
period
less than a fixed threshold T*.
o Mutually exclusive projects: take the project with the
lowest payback period.
2010 / Yichuan Liu
6
Review: payback period

Pro:
o Easy to calculate

Con:
o Ignores cashh flows
fl
after
f the
h payback
b k period
d
o Ignores time value of money

Discounted payback period: minimum T such that
T
CFt
 CF0  I 0

t
t 1 1 rt 
o Problem: still ignores cash flows after the payback period
2010 / Yichuan Liu
7
Review: IRR

The internal rate of return (IRR) is the discount rate
that satisfies

CFt
0


t


1

IRR
t 0
IRR is the implied rate of return of the project.
 Decisi
D i ion rule:
l

o Independent projects: take the projects with IRR > r*,
where r* is the required rate of return.
o Mutually exclusive projects: take the project with the
highest IRR (provided it is greater than r*).
2010 / Yichuan Liu
8
Review: IRR

IRR gives the same decision as NPV if
o Cash outflow occurs only at time 0
o Only one project is under consideration
o Required
R
i d costt off capital
it l iis th
the same ffor allll periods
i d
o Threshold rate is set to the required cost of capital

Potential problem:
o IRR may not exist
o There may be multiple IRRs for a single cash flow.
o IRR rule gives the wrong decision for mutually exclusive
projects.
2010 / Yichuan Liu
9
Review: profitability index

The profitability index of a project is
1
PI 
I0


CFt

t
t 1 1 rt 
Decision rule:
o Independent projects: take all projects with PI > 1.
o Mutually exclusive projects: take the project with the
highest PI.

PI gives the same decision as NPV if
o Cash outflow occurs only at time 0
o There is only one project under consideration.
2010 / Yichuan Liu
10
Example: Bart’s Super‐Widget

Project overview:
o Bart Co., a profitable widget maker, has developed an
innovative new product called the Super‐Widget. The
company has investted
d $300,000
$
in R&D to
t devellop th
the
product and expects that it will capture a large share of
the market.

Capital requirement:
o Bart Co. will have to invest $750,000 in new equipment.
The machines have a useful life of 5 years,
years with an
expected salvage value of $0.
Courtesy of Bart Raeymaekers. Used with permission.
2010 / Yichuan Liu
11
Example: Bart’s Super‐Widget

Revenue projection:
o Over the next five years, unit sales are expected to be (5,
8, 12, 10, 6) thousand units.
o Prices
Pi
i the
in
th first
fi t year will
ill b
be $
$480,
8 and
d then
th will
ill grow 2%
%
annually.

Op
perating
g exp
penses:
o Sales and administrative costs will be $150,000/year.
o Production costs will be $500/unit in the first year, but will
decline byy 8% everyy yyear thereafter.
o The tax rate is 35% and the after‐tax cost of capital is 12%.
Courtesy of Bart Raeymaekers. Used with permission.
2010 / Yichuan Liu
12
Example: Bart’s Super‐Widget

Revenue and Cost
Revenue
Units
Price/Unit
Total
Expenses
SG&A
Cost/Unit
Total
Op. Profit
t=1
2
3
4
5
5,000
480
2,400,000
8,000
490
3,916,800
12,000
499
5,992,704
10,000
509
5,093,798
6,000
520
3,117,405
150,000
150,000
150,000
150,000
150,000
500
460
423
389
358
(2,650,000) (3,830,000) (5,228,400) (4,043,440) (2,299,179)
(250,000)
86,800
764,304
1,050,358
818,226
Courtesy of Bart Raeymaekers. Used with permission.
2010 / Yichuan Liu
13
Example: Bart’s Super‐Widget

Dep
preciation and Tax
Op. Profit
Depreciation
EBIT
Taxes @35%
Net income
2010 / Yichuan Liu
t=1
(250,000)
(150,000)
(400,000)
140,000
(260,000)
2
86,800
(150,000)
(63,200)
22,120
(41,080)
3
764,304
(150,000)
614,304
(215,006)
399,298
4
1,050,358
(150,000)
900,358
(315,125)
585,233
5
818,226
(150,000)
668,226
(233,879)
434,347
14
Example: Bart’s Super‐Widget

Cash Flow
t=0
Net income
1
2
3
4
5
(260,000))
(260,000
(41,080))
(41,080
399,298
585,233
434,347
CAPEX
(1,000,000)
Cash flow
(1,000,000)
(110,000)
108,920
549,298
735,233
584,347
PV @ 12%
(1,000,000)
(98,214)
86,830
390,979
467,254
331,574
NPV
2010 / Yichuan Liu
$178,423
15
Example: Bart’s Super‐Widget

Reminder:
o CF = after‐tax operating income + depreciation tax shield
– capital expenditure
= (1 – τ) x operating income + τ x depreciation
– capital expenditure
o The accounting net income is taxed even if it is negative.
o Deppreciation is not a cash flow but reduces taxes.
2010 / Yichuan Liu
16
MIT OpenCourseWare
http://ocw.mit.edu
15.401 Finance Theory I
Fall 2008
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